Your comments:

Further to Jon Wayre's recollections which I tend to agree with, I have one of these pantographs and it has what looks like a purpose made platform with a spring loaded retaining slider which is the right size for a rectangular base telephone such as a pyramid model.
Nigel Williams. Colchester .......... Nigel Williams, Colchester, United Kingdom, 12th of April 2013

The Trade mark stamped on the side of the unit states 'Walligraph Registered Trade Mark Telephone Arm' .......... Curator Museum of Technology, Hemel Hempstead, 7th of September 2010

My father worked for Walligraph in the 1940s/50s.
Walligraph produced industrial lamps for use in factories, workshops, et c. What this actually is, is a Wally Pantograph lamp holder that has had the lamp replaced with a candlestick phone. It looks good and fits the phone perfectly but is something that must have been made up by someone as I own a few lamps and have several brochures of the Pantograph and there is no mention of a telephone model. .......... Jon Wayre, London, 6th of September 2010